CHAPTER 8
 ORTHOGONAL MANIPULATORS



 Definition: An n-axes, serial kinematic chain of revolute or prismatic joints is orthogonal if all twist angles ai, i=l, . n, along the chain are 0 or v/2. An open orthogonal kinematic chain will be called an orthogonal manipulator (Doty 1986).

 Six-DOF orthogonal manipulators can be classified in terms of the values of their twist angles ai, i=l, . 5. Twist angle a6 is always assumed to be zero in this text. In fact, the value of a6 can be chosen arbitrarily since z6 is not a joint axis. Therefore, there are only 25 = 32 distinct classes of orthogonal manipulators, as listed in Table 8-1, 8 of which have 4 or more adjacent parallel joint axes which reduces their capability to less than six degrees of freedom. As a result, there are only 24 types of. six-joint orthogonal manipulators with full spatial position and orientation capability.

 A convenient notation for this classification of orthogonal manipulators is obtained by assigning a 5-bit binary number to each of these 24 types in which bit i is 0 if ai= 0 and bit i is 1 if ai=7r/2. For example, a

manipulator with twist angles'

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